Nonlinear hydrodynamic interface instabilities driven by time-dependent accelerations

We present a model for nonlinear hydrodynamic instabilities of interfaces and the formation of bubbles driven by time-dependent accelerations g(t) . To obtain analytic solutions, we map the equation for the bubble amplitude eta(t) onto the Schrödinger equation and solve it as an initial value (eta₀,eta[over ]₀) problem in time instead of an eigenvalue problem in space. Very good agreement is obtained with full hydrodynamic simulations. We then apply the WKB approximation to derive scaling with s=integralsqrt[g(t)]dt . Bubbles scale while spikes do not. Zitterbewegung, meaning rapid oscillations of g(t) around an average value, has little effect on eta(t) .